The web exercise
Graphs of Functions
in the
Algebra II curriculum
gives a thorough introduction to graphs of functions.
For those who need only a quick review,
the key concepts are repeated here.
The exercises on this current web page duplicate those in
Graphs of Functions.
There are things that you can DO to an equation $\,y = f(x)\,$ that will change its graph.
Or, there are things that you can DO to a graph that will change
its equation.
Stretching, shrinking, moving up/down/left/right, reflecting about axes;
they're all covered thoroughly in the next few web exercises:
An understanding of these graphical transformations makes it easy to graph a
wide variety of functions,
by starting with a basic model and
then applying a sequence of transformations to change it to the desired function.
For example, after mastering the graphical transformations, you'll be able to do the following:
For your convenience, all the graphical transformations are summarized in the
GRAPHICAL TRANSFORMATIONS table below.
Given any entry in a row, you should (eventually!) be able to
fill in all the remaining entries in that row.
TRANSFORMATIONS INVOLVING $\,\boldsymbol{y}$ (note that transformations involving $\,y\,$ are intuitive) 

DO THIS TO THE PREVIOUS $y$VALUE  NEW EQUATION  NEW GRAPH  $(a,b)$ MOVES TO ...  TRANSFORMATION TYPE 
add $\,p$ subtract $\,p$ 
$y = f(x) + p$ $y = f(x)  p$ 
shifts $\,p\,$ units UP shifts $\,p\,$ units DOWN 
$(a,b+p)$ $(a,bp)$ 
vertical translation vertical translation 
multiply by $\,1$  $y = f(x)$  reflect about $x$axis  $(a,b)$  reflection about $x$axis 
multiply by $\,g$  $y = g\cdot f(x)$  vertical stretch by a factor of $\,g$ 
$(a,gb)$  vertical stretch/elongation 
divide by $\,g$  $\displaystyle y = \frac{f(x)}{g}$  vertical shrink by a factor of $\,g$ 
$\displaystyle \bigl(a,\frac{b}{g}\bigr)$  vertical shrink/compression 
take absolute value  $y = f(x)$  part below $x$axis flips up  $(a,b)$  absolute value 
TRANSFORMATIONS INVOLVING $\,\boldsymbol{x}$ (note that transformations involving $\,x\,$ are counterintuitive) 

REPLACE ...  NEW EQUATION  NEW GRAPH  $(a,b)$ MOVES TO ...  TRANSFORMATION TYPE 
every $\,x\,$ by $\,x+p\,$ every $\,x\,$ by $\,xp$ 
$y = f(x+p)$ $y = f(xp)$ 
shifts $\,p\,$ units LEFT shifts $\,p\,$ units RIGHT 
$(ap,b)$ $(a+p,b)$ 
horizontal translation horizontal translation 
every $\,x\,$ by $\,x\,$  $y = f(x)$  reflect about $y$axis  $(a,b)$  reflection about $y$axis 
every $\,x\,$ by $\,gx\,$  $y = f(gx)$  horizontal shrink by a factor of $\,g$ 
$\displaystyle \bigl(\frac{a}{g},b\bigr)$  horizontal shrink/compression 
every $\,x\,$ by $\,\displaystyle \frac{x}{g}\,$  $\displaystyle y = f\bigl(\frac{x}{g}\bigr)$  horizontal stretch by a factor of $\,g$ 
$(ga,b)$  horizontal stretch/elongation 
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
